19-nor C3, 3-disubstituted C21-C-bound heteroaryl steroids and methods of use thereof

1. A method for positively modulating a GABA A receptor in a human subject in need thereof, comprising administering to the human subject an effective amount of a) a compound of the formula (I) or a pharmaceutically acceptable salt thereof or b) a pharmaceutical composition comprising a compound of formula (I) or a pharmaceutically acceptable salt thereof and a pharmaceutically acceptable excipient, wherein:

represents a single or double bond;

R 1 is substituted or unsubstituted C 1-6 alkyl, substituted or unsubstituted C 2-6 alkenyl, substituted or unsubstituted C 2-6 alkynyl, or substituted or unsubstituted C 3-6 carbocyclyl;

R 2 is hydrogen, halogen, substituted or unsubstituted C 1-6 alkyl, substituted or unsubstituted C 2-6 alkenyl, substituted or unsubstituted C 2-6 alkynyl, substituted or unsubstituted C 3-6 carbocyclyl, or —OR A2 , wherein R A2 is hydrogen or substituted or unsubstituted C 1-6 alkyl, substituted or unsubstituted C 2-6 alkenyl, substituted or unsubstituted C 2-6 alkynyl, or substituted or unsubstituted C 3-6 carbocyclyl;

R 3a is hydrogen or —OR A3 , wherein R A3 is hydrogen or substituted or unsubstituted C 1-6 alkyl, substituted or unsubstituted C 2-6 alkenyl, substituted or unsubstituted C 2-6 alkynyl, or substituted or unsubstituted C 3-6 carbocyclyl, and R 3b is hydrogen; or R 3a and R 3b are joined to form an oxo (═O) group;

each instance of R 4a and R 4b is independently hydrogen, substituted or unsubstituted C 1-6 alkyl, or halogen, provided if the between C5 and C6 is a single bond, then the hydrogen at C5 and R 4a are each independently provided in the alpha or beta configuration, and when is a double bond, then the hydrogen at C5 and R 4b are absent;

A is a carbon bound substituted or unsubstituted 5 or 6-membered heteroaryl, or 6-membered aryl of formula:

X is —O—, —S—, or —N(R N )—, wherein R N is independently hydrogen, substituted or unsubstituted C 1-6 alkyl, —C(═O)R GA , —C(═O)OR GA , —C(═O)N(R GA ) 2 , —S(═O) 2 R GA , —S(═O) 2 OR GA , —S(═O) 2 N(R GA ) 2 , or a nitrogen protecting group;

each instance of R 5 , R 6 , R 7 , R 8 , and R 9 is, independently, hydrogen, halogen, —NO 2 , —CN, —OR GA , —N(R GA ) 2 , —C(═O)R GA , —C(═O)OR GA , —OC(═O)R GA , —OC(═O)OR GA , —C(═O)N(R GA ) 2 , —N(R GA )C(═O)R GA , —OC(═O)N(R GA ) 2 , —N(R GA )C(═O)OR GA , —N(R GA )C(═O)N(R GA ) 2 , —S(═O) 2 R GA , —S(═O) 2 OR GA , —OS(═O) 2 R GA , —S(═O) 2 N(R GA ) 2 , —N(R GA )S(═O) 2 R GA , substituted or unsubstituted C 1-6 alkyl, substituted or unsubstituted C 2-6 alkenyl, substituted or unsubstituted C 2-6 alkynyl, substituted or unsubstituted C 3-6 carbocylyl, or substituted or unsubstituted 3- to 6-membered heterocylyl; and

each instance of R GA is independently hydrogen, substituted or unsubstituted C 1-6 alkyl, substituted or unsubstituted C 2-6 alkenyl, substituted or unsubstituted C 2-6 alkynyl, substituted or unsubstituted C 3-6 carbocylyl, substituted or unsubstituted 3- to 6-membered heterocylyl, substituted or unsubstituted aryl, substituted or unsubstituted heteroaryl, an oxygen protecting group when attached to oxygen, nitrogen protecting group when attached to nitrogen, or two R GA groups are taken with the intervening atoms to form a substituted or unsubstituted heterocylyl or heteroaryl ring.

2. The method of claim 1 , wherein the compound is a compound of Formula (I-A):

3. The method of claim 1 , wherein R 1 is —CH 3 , —CH 2 CH 3 , —CH 2 F, —CHF 2 , —CF 3 , —CH 2 OCH 3 , or substituted or unsubstituted cyclopropyl.

4. The method of claim 3 , wherein R 1 is —CH 3 .

5. The method of claim 1 , wherein R 2 is hydrogen.

6. The method of claim 1 , wherein R 3a and R 3b are both hydrogen.

7. The method of claim 1 , wherein represents a single bond, and both of R 4a and R 4b are hydrogen.

8. The method of claim 1 , wherein represents a single bond, and both of R 4a and R 4b are fluoro.

9. The method of claim 1 , wherein at least one of R 5 , R 6 , R 7 , R 8 , and R 9 is substituted or unsubstituted C 1-2 alkyl, —CO 2 R GA , —C(═O)R GA , —CN, —NO 2 , or halogen, wherein R GA is substituted or unsubstituted C 1-2 alkyl.

10. The method of claim 9 , wherein at least one of R 5 , R 6 , R 7 , R 8 , and R 9 is substituted or unsubstituted —CH 3 .

11. The method of claim 1 , wherein R 5 , R 6 , R 7 , R 8 , and R 9 are hydrogen.

12. The method of claim 1 , wherein the compound is a compound of Formula (I-A-i):

13. The method of claim 1 , wherein A is:

14. The method of claim 12 , wherein the compound is selected from the group consisting of:

and pharmaceutically acceptable salts thereof.

15. The method of claim 1 , wherein the human subject has a CNS-related disorder.

16. The method of claim 15 , wherein the CNS-related disorder is a sleep disorder, a mood disorder, a schizophrenia spectrum disorder, a convulsive disorder, a disorder of memory and/or cognition, a movement disorder, a personality disorder, autism spectrum disorder, pain, traumatic brain injury, a vascular disease, a substance abuse disorder and/or withdrawal syndrome, or tinnitus.

17. The method of claim 16 , wherein the mood disorder is depression.

18. The method of claim 17 , wherein the depression is postnatal depression.

19. The method of claim 16 , wherein the sleep disorder is insomnia.

20. The method of claim 16 , wherein the compound is administered orally, subcutaneously, intravenously, or intramuscularly.